1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* tan(x)
13 * Return tangent function of x.
14 *
15 * kernel function:
16 * __kernel_tan ... tangent function on [-pi/4,pi/4]
17 * __ieee754_rem_pio2 ... argument reduction routine
18 *
19 * Method.
20 * Let S,C and T denote the sin, cos and tan respectively on
21 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
22 * in [-pi/4 , +pi/4], and let n = k mod 4.
23 * We have
24 *
25 * n sin(x) cos(x) tan(x)
26 * ----------------------------------------------------------
27 * 0 S C T
28 * 1 C -S -1/T
29 * 2 -S -C T
30 * 3 -C S -1/T
31 * ----------------------------------------------------------
32 *
33 * Special cases:
34 * Let trig be any of sin, cos, or tan.
35 * trig(+-INF) is NaN, with signals;
36 * trig(NaN) is that NaN;
37 *
38 * Accuracy:
39 * TRIG(x) returns trig(x) nearly rounded
40 */
41
42 #include "math_libm.h"
43 #include "math_private.h"
44
tan(double x)45 double tan(double x)
46 {
47 double y[2],z=0.0;
48 int32_t n, ix;
49
50 /* High word of x. */
51 GET_HIGH_WORD(ix,x);
52
53 /* |x| ~< pi/4 */
54 ix &= 0x7fffffff;
55 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
56
57 /* tan(Inf or NaN) is NaN */
58 else if (ix>=0x7ff00000) return x-x; /* NaN */
59
60 /* argument reduction needed */
61 else {
62 n = __ieee754_rem_pio2(x,y);
63 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
64 -1 -- n odd */
65 }
66 }
67 libm_hidden_def(tan)
68